Problems to Ponder (July edition)

Welcome to this month’s edition of Problems to Ponder! Pose them in your classroom as a challenge or try them out yourself. Have an interesting solution? Send it to thevariable@smts.ca for publication in a future issue ofThe Variable,our monthly periodical.

The sixth cent

You toss a fair coin 6 times, and I toss a fair coin 5 times. What is the probability that you get more heads than I do?

Consider the following four dice, which have the following numbers on their faces:

Red : 0, 1, 7, 8, 8, 9

Blue: 5, 5, 6, 6, 7, 7

Green: 1, 2, 3, 9, 10, 11

Black: 3, 4, 4, 5, 11, 12

The dice are used to play the following game for two people. Player 1 chooses a die, then Player 2 chooses a die. Then, each player rolls their die. The player with the highest number showing gets a point. The first player to get 7 points wins the game. If you are Player 1, which die should you choose? If you are Player 2, which die should you choose?

Two too many diceSuppose you have a clear, sealed cube containing three smaller, indistinguishable six-sided dice. How can you use this three-in-one die to simulate a single, six-sided die? (Bonus: How can you use the three-in-one die to simulate two six-sided dice?)

Adapted from Parker, M. [standupmaths]. (2016, April 12). The three indistinguishable dice puzzle. Retrieved from https://youtu.be/xHh0ui5mi_E